Perturbative global solutions of a large class of cross diffusion systems in any dimension
Abstract
This article focuses on a large family of cross-diffusion systems of the form ∂ t U-(U) = 0, in dimension d ∈ N * , and where U ∈ R 2. We show that under natural conditions on the nonlinearity A, those systems have a unique smooth (nonnegative for all components) solution when the initial data are small enough in a suitable norm.
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